An analytic language is any language where syntax and meaning are shaped more by use of particles and word order than by inflection. The opposite of an analytic language is a synthetic language.
A related, often-confused concept is that of an isolating language. An isolating language is any language where the vast majority of morphemes are free morphemes and are considered to be full-fledged "words". The degree of isolation is defined by the morphemes-per-word ratio. By contrast, in a synthetic language, words are composed of agglutinated or fused morphemes that denote their syntactic meanings.

Features of analytic languages
Analytic languages often express abstract concepts using independent words, while synthetic languages tend to use adpositions, affixes and internal modifications of roots for the same purpose.
Analytic languages have stricter and more elaborate syntactic rules. Since words are not marked by morphology showing their role in the sentence, word order tends to carry a lot of importance; for example, Chinese and English make use of word order to show subject-object relationship. Chinese also uses word order to show definiteness (where English uses "the" and "a"), topic-comment relationships, the role of adverbs (whether they are descriptive or contrastive), and so on.
Analytic languages tend to rely heavily on context and pragmatic considerations for the interpretation of sentences, since they don't specify as much as synthetic languages in terms of agreement and cross-reference between different parts of the sentence.
Chinese (of all varieties) is perhaps the best-known analytic language. To illustrate:
As can be seen, each syllable (or sometimes two) corresponds to a single concept; comparing the Chinese to the English translation, one sees that while English itself is still fairly isolating, it contains synthetic features, such as the bound morpheme -/s/ to mark either possession (in the form of a clitic) or number (in the form of a suffix). Further, note that the English verb is independently conjugated into a tense ("will make") indicating that the action will happen in the future. In contrast, the Chinese verb (zuò) is not inflected, and relies on other words to indicate tense (in this case the words míngtīan [tomorrow] and hui [will]).
"zuò" (do) remains the same in the present tense:
Outside of China, the majority of mainland Southeast Asian languages are analytic languages with the exception of Malay. Mainland Southeast Asia is home to much of eastern Asia's analytic language families including Tibeto-Burman, Tai-Kadai, Hmong-Mien and Mon-Khmer. Even some Malayo-Polynesian languages such as Cham are more analytic than the rest of their respective family. Burmese, Thai, Khmer, Lao and Vietnamese are all major analytic languages spoken in mainland southeast Asia.
When compared with a synthetic language, such as German, the contrast becomes clear:
Note that the morpheme "der" corresponds to four separate concepts simultaneously, and the morpheme "die" refers to three concepts (German does not distinguish gender in the plural), but the rules relating "der" and "die" in this manner are quite arbitrary, making this set of morphemes fusional in nature. It is worth mentioning that both "der" and "die" can function as a feminine singular definite article, depending on the grammatical case. Furthermore, the word "Männer" corresponds to two concepts and relates to "Mann" through both the plural marker /-er/ and a process of umlaut that changes "a" to "ä" in many German plurals. Thus, the formation of German plurals is a simple, rule-governed inflectional pattern.
As a result, German can be said to lie between the agglutinative and fusional areas of the spectrum of linguistic typology.